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Paper 2020/293

"Many-out-of-Many" Proofs with Applications to Anonymous Zether

Benjamin E. Diamond

Abstract

We introduce a family of extensions to the one-out-of-many proofs of Groth and Kohlweiss (Eurocrypt 2015), which efficiently prove statements about many messages among a list of commitments. These extensions prove knowledge of a secret subset of the list, and assert that the commitments in the subset satisfy certain properties (expressed as linear equations). Our communication remains logarithmic; our computation increases only by a logarithmic multiplicative factor. Our work introduces a new "circular rotation" technique, and a novel instantiation of the number-theoretic transform. Applying these techniques, we construct a protocol for the Anonymous Zether payment system—as proposed in Bünz, Agrawal, Zamani, and Boneh (FC'20)—which improves upon the communication complexity attained by existing efforts. We describe an open-source, Ethereum-based implementation of our protocol.

Metadata
Available format(s)
PDF
Category
Cryptographic protocols
Publication info
Preprint. MINOR revision.
Keywords
anonymitycombinatorial cryptographyelectronic commerce and paymentzero knowledge
Contact author(s)
benediamond @ gmail com
History
2020-10-26: last of 2 revisions
2020-03-06: received
See all versions
Short URL
https://ia.cr/2020/293
License
Creative Commons Attribution
CC BY
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